Optimal. Leaf size=27 \[ -\frac {F^{a+\frac {b}{(c+d x)^3}}}{3 b d \log (F)} \]
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Rubi [A] time = 0.04, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2209} \[ -\frac {F^{a+\frac {b}{(c+d x)^3}}}{3 b d \log (F)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin {align*} \int \frac {F^{a+\frac {b}{(c+d x)^3}}}{(c+d x)^4} \, dx &=-\frac {F^{a+\frac {b}{(c+d x)^3}}}{3 b d \log (F)}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 1.00 \[ -\frac {F^{a+\frac {b}{(c+d x)^3}}}{3 b d \log (F)} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.42, size = 77, normalized size = 2.85 \[ -\frac {F^{\frac {a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}}}{3 \, b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.48, size = 77, normalized size = 2.85 \[ -\frac {F^{\frac {a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}}}{3 \, b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 26, normalized size = 0.96 \[ -\frac {F^{a +\frac {b}{\left (d x +c \right )^{3}}}}{3 b d \ln \relax (F )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 25, normalized size = 0.93 \[ -\frac {F^{a + \frac {b}{{\left (d x + c\right )}^{3}}}}{3 \, b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.64, size = 48, normalized size = 1.78 \[ -\frac {F^a\,F^{\frac {b}{c^3+3\,c^2\,d\,x+3\,c\,d^2\,x^2+d^3\,x^3}}}{3\,b\,d\,\ln \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 66, normalized size = 2.44 \[ \begin {cases} - \frac {F^{a + \frac {b}{\left (c + d x\right )^{3}}}}{3 b d \log {\relax (F )}} & \text {for}\: 3 b d \log {\relax (F )} \neq 0 \\- \frac {1}{3 c^{3} d + 9 c^{2} d^{2} x + 9 c d^{3} x^{2} + 3 d^{4} x^{3}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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